The invention refers to methods for the acquisition of mass spectra with ultra-high mass resolution in ion cyclotron resonance measuring cells. In ion cyclotron resonance mass spectrometers (ICR-MS), the charge-related masses m/z of the ion species are measured by measuring the cycling frequencies of clouds of these ion species cycling coherently in ICR measuring cells; these clouds are located in a homogenous magnetic field of high strength. The cycling motion consists of a superposition of cyclotron and magnetron motions. The magnetic field is usually created by superconducting magnet coils cooled with liquid helium. Commercial mass spectrometers nowadays offer usable diameters of ICR measuring cell up to about 6 centimeters with magnetic field strengths of between 7 and 15 tesla.
The ion cycling frequency is measured in the ICR measuring cell in the most homogenous part of the magnetic field. ICR measuring cells made according to existing technology generally consist of four longitudinal electrodes extending parallel to the magnetic field lines and enclosing the inner region of the measuring cell as a cylindrical jacket. Cylindrical measuring cells, as illustrated in FIG. 1, are used most often. Ions are usually introduced close to the axis. Two electrodes on opposite sides of the cell are used to excite these ions into cyclotron motion on larger orbits; ions having the same charge-related mass m/z are excited as coherently as possible, in order to obtain a cloud of these ions cycling in phase. The other two electrodes are used to measure the cycling frequency of the clouds of ions by their image currents, which are induced in the electrodes as the ion clouds fly by. The measuring cell is filled with ions; the ions are excited and are then detected in a sequence of procedural phases, as is known to every technical expert in the field.
Because the ratio m/z of the mass m to the number z of elementary charges on each ion (here referred to simply as “charge-related mass”, or sometimes simply just as “mass”) is unknown before measured, the ions are excited by a homogenous mixture of excitation frequencies. The mixture here can be distributed over time, with frequencies that rise by time (this is usually referred to as a “chirp”), or it can be a synchronous mixture of all frequencies calculated by computer (a “sync pulse”).
The image current induced in the detection electrodes by the cycling ion clouds constitutes, as a function of time, a so-called “transient”. The transient is a signal in the “time domain”, and usually decreases within a few seconds until only noise remains. In measuring cells of classic design, durations of the usable transients show a maximum of about four seconds. When the simple term “duration” is used below in connection with a transient, always the “useful duration” until only noise remains is meant.
The image currents of these transients are amplified, digitized and then subjected to Fourier analysis to determine the cycling frequencies of the ion clouds of various masses contained within them. The Fourier analysis transforms the sequence of the image current values measured originally for the transients from the “time domain” into a sequence of frequency values in the “frequency domain”. The charge-related mass m/z and their intensities are determined from the peaks of the frequency signals for the various ion species detectable in the frequency domain. As a result of the highly constant magnetic fields used, and of the high precision with which frequency measurements can be obtained, an extremely precise determination of the mass can be achieved. ICR-MS is also referred to as “Fourier transform mass spectrometry” (FTMS), although it should be noted that nowadays other types of FTMS are known that are not based on the cycling of ions in magnetic fields. At present, Fourier transform ICR mass spectrometry (properly abbreviated to FT-ICR-MS) is the most accurate of all mass spectrometry methods. The precision with which the mass can be determined ultimately depends on the number of ion circulations that can be acquired during the measurement.
When the term “acquiring an ICR mass spectrum” or a similar formulation is used below, this includes, as any technical expert knows, the full sequence of steps from filling the ICR measuring cell with ions, exciting the ions to cyclotron motion, measuring the image current transients, digitization, Fourier transformation, determination of the frequencies of the individual ion species, and finally calculation of the charge-related masses and the intensities of the ion species represented in the mass spectrum.
In order to introduce the ions into the ICR measuring cell, and particularly in order to confine them, a variety of methods such as, for instance, the “side-kick” method or the method of dynamic confinement through rising potentials are known, but these will not be discussed in more detail here. The technical expert in this field is familiar with these methods.
Accurate and precise mass determination is extremely important in modern biological mass spectrometry. No limit is known for the mass precision beyond which no further increase in the information content could be expected. Increasing mass precision is therefore a target to be pursued continuously. A high mass precision alone, however, is often not sufficient to solve a given analytical task. In addition to a highly precise measurement of mass, a high mass resolving power is particularly critical, since, above all in biological mass spectrometry, it is often necessary to separately detect and measure ion signals with very small differences in mass. For instance, the enzymatic digestion of mixtures of proteins gives rise to thousands of ion species in one mass spectrum; it is often necessary to separate and accurately measure five, ten or more different ion species in a small interval around a nominal mass number.
In the cylindrical measuring cells that are used today, the cell is formed from four longitudinal electrodes, as illustrated in FIG. 1. Cylindrical measuring cells are used most frequently, primarily because they offer the best possible exploitation of the volume in the magnetic field from a round coil. The image currents from tight clouds of ions of one mass generate a curve with almost rectangular amplitudes when they move close to the detection electrodes. But the smearing of the ion clouds always observed until now on the one hand, and the distance of the ion circulation tracks from the detection electrodes selected by the excitation conditions on the other hand, result in substantially sinusoidal image current signals for each ion species, from which a Fourier analysis can easily determine the cycling frequency and therewith the mass.
Because the ions can move freely in the direction of the magnetic field lines, it is necessary to prevent the ions from leaving the measuring cell. The ions always have a velocity component in the magnetic field direction from their capturing process. For this reason, the two ends of the measuring cell are fitted with electrodes known as “trapping electrodes”. DC potentials are usually applied to them to repel the ions and hold them inside the measuring cell. Various shapes are known for this electrode pair; in the simplest case, they are planar and have a central hole, as shown in FIG. 1. The hole is used to insert the ions into the measuring cell. In other cases, further electrodes with the shape of cylindrical jacket segments are attached beyond the ends of the measuring cell, continuing the central cylinder jacket segments at both ends, and with trapping voltages applied to them. This then creates an open cylinder without cylinder covers at the ends, as shown in FIG. 2; these are referred to as “open ICR cells”.
Looking at the potential distribution along the axis of the measuring cell, the ion-repelling potentials of the outer trapping electrodes (compared to the potential of the longitudinal electrodes) create a potential well in the centre of the measuring cell, both in the case of apertured diaphragms and of open ICR cells. The curve of the potential along the axis has a minimum precisely in the centre of the measuring cell if the potentials of the two trapping electrodes that repel the ions are equal in magnitude; in the immediate neighborhood of the centre this potential curve is parabolic, and therefore harmonic. At greater distances from the centre, the potential curve deviates increasingly from the parabolic form. The injected ions will execute axial oscillations in this potential well, the so-called trapping oscillations, as they have a velocity in the axial direction resulting from their injection. Provided the ions are not given any additional kinetic energy in radial direction, the strong magnetic field holds the ions on the axis, preventing any radial deviation.
The amplitude of the trapping oscillations depends on the kinetic energy associated with their axial velocity. If the amplitudes are small enough that the ions do not leave the strictly parabolic region of the potential minimum, their oscillation is “harmonic”, in which case the oscillation frequency does not depend on its amplitude. This is no longer true for larger oscillation amplitudes that take the ions beyond the parabolic region of the potential minimum; in this case the oscillation frequency depends on the amplitude.
It should, however, also be noted here that while the trapping potentials have a minimum along the axis, the potentials in the radial direction fall away towards the longitudinal electrodes. The minimum in the axial direction is, considered in three dimensions, a saddle; the trapping potential falls radially, i.e. perpendicular to the axis, towards every side. In three dimensions, the precise shape of the potential distribution forms a spatial quadrupole field, at least in the immediate neighborhood of the saddle. As has already been mentioned, the ions that are introduced to the axis are unable to deviate to the sides due to the strong magnetic field until they absorb additional energy from oscillating electrical excitation fields and are lifted onto the cyclotron tracks.
The trapping potentials that are the cause of the trapping oscillations change the frequencies of the cycling motion of the ions, and therefore have an effect on the determination of mass. The measured orbit frequency ω+ (the “reduced cyclotron frequency”) of an ion species in the absence of additional space charge effects, i.e. when there are only very few ions in the ICR measuring cell, is given by
            ω      +        =                            ω          c                2            +                                                  ω              c              2                        4                    -                                    ω              t              2                        2                                ,where ωc is the undisturbed cyclotron frequency, and ωt is the frequency of the trapping oscillation. It can be seen from this that it is favorable for the trapping oscillations to provide a harmonic electrical trapping potential with a potential well that is precisely parabolic even well beyond the centre, as only then the frequency ωt of the trapping oscillations, and therefore of the measured orbit frequency ω+, is well-defined. It is therefore favorable to have an accurately quadrupolar potential distribution even well away from the centre. It is only if the frequency ωt of the trapping oscillations is well-defined and independent of its (accidental) oscillation amplitude that the reduced cyclotron frequency ω+ is also well-defined and that high precision can be expected from the charge-related mass m/z that is determined from it.
The frequency ωt of the trapping oscillations affects the reduced cyclotron frequency ω+ through a somewhat complicated mechanism. When the ions are excited through circular accelerations into cyclotron motion, the electrical field components of the trapping field in a radial direction generate a second type of motion in the ions: circular magnetron motion. Magnetron circulation is a circular movement around the axis of the measuring cell, but is usually much slower than circular cyclotron movement and, following successful excitation, has a much smaller radius. The effect of the additional magnetron circulation is that the centre of the circular cyclotron movements moves around the axis of the measuring cell at the magnetron frequency, so that the tracks of the ions describe cycloidal motions. Only through this magnetron circulation does the trapping field have an effect on the cyclotron movement, resulting in a reduced cyclotron frequency ω+.
There is agreement amongst most experts that in order to provide the most ideally harmonic trapping oscillations possible, an ideal trapping potential should adopt the form of a three-dimensional quadrupolar field as accurately as possible even outside the immediate vicinity of the centre. Excited ions can then oscillate harmonically, parallel to the axis of the measuring cell, even during their cyclotron motion. A quadrupolar trapping field of this sort can most easily be generated by rotationally hyperbolic end cap and ring electrodes, geometrically similar to those of a three-dimensional Paul high-frequency quadrupole ion trap; but then acceleration to cyclotron motion is difficult.
The design of an ICR measuring cell for proper function therefore involves a difficult dilemma. On the one hand, the demand for a quadrupolar distribution of the trapping potentials calls for a measuring cell that can optimally be made only with rotationally hyperbolic end cap and ring electrodes; on the other hand, exciting the ions in an extended ion cloud to cyclotron motion demands for very long electrodes parallel to the axis. It is very difficult to satisfy both of these demands at the same time.
A practical solution was first published in the work of G. Gabrielse et al., “Open-Endcap Penning Traps for High Precision Experiments”, (I J Mass Spectrom & Ion Processes, 88 (1989), 319-332). The authors introduced compensation electrodes into an open ICR measuring cell. Measuring cells with five segments were described, with which, according to mathematical calculations, good approximations to broad quadrupolar trapping fields could be achieved.
There have recently been two further attempts to create trapping potentials in open ICR measuring cells that reproduce as closely as possible the three-dimensional quadrupolar field of an ideal ICR measuring cell in a larger area around the centre, in order to generate harmonic trapping oscillations. In both papers, the approaches to solve the dichotomy between hyperbolic and cylindrical measuring cells again were made with the aid of compensation electrodes; more compensation electrodes were used here than were by Gabrielse et al. In both of these projects, the favorable potentials at the compensation electrodes were determined through computer simulations.
In the paper by A. V. Tolmachev et al., “Trapped-Ion Cell with Improved DC Potential Harmonicity for FT-ICR MS” (J Am Soc Mass Spectrom 2008, 19, 586-597) an attempt was described to optimize the DC potentials in a measuring cell simulated in a computer, using electrode segments of given widths in order to achieve the smallest possible deviations from the theoretical values of a quadrupolar distribution for the radial potential E/r, normalized to the radius r, over a broad region around the centre. Both for the purposes of simulation and later in the construction of a real measuring cell, seven segments with relative widths of 10, 2, 2, 5, 2, 2, and 10, each having four longitudinal electrodes were used, together creating a long cylinder with a total of 4×7=28 longitudinal electrodes. In order to excite the ions into cyclotron motion, two ensembles of longitudinal electrodes extending across all seven segments were used. The DC potentials that had been found optimal in the simulation were used for measurements using the physically constructed measuring cell. The mass precision that could be achieved with this measuring cell was in fact outstanding at 50 ppb (parts per billion), although only relatively short segments of the transients, with a maximum of just two seconds, but in most cases only between 0.2 and 0.5 seconds, were used for the Fourier transformations. Nothing was reported about the mass resolutions; however, with such short transient periods they cannot be extraordinarily high, as the mass resolution is always proportional to the number of oscillation periods measured.
Another attempt to minimize the deviations between simulated and ideal quadrupole fields as effectively as possible was made in the work of A. M. Brustkern et al., “An Electrically Compensated Trap Designed to Eighth Order for FT-ICR Mass Spectrometry”, (J Am Soc Mass Spectrom 2008, 19, 1281-1285), again using the field of a simulated measuring cell, but in this case having a total of nine segments. The three compensation electrodes used on each side of the central segment were very narrow here. Unfortunately, the work does not report any exact measurement parameters for the mass spectrometry experiments; among other things it can only be assumed that cooled ion clouds were used, generated by pulses of injected nitrogen and then in part excited again into coherent trapping oscillations. The reported mass resolution of 17 million for [Arg8]-vasopressin with a mass of 1084.5 dalton can, in all probability however, be traced to a peak coalescence (see below) or to an associated “phase locking”; these must be avoided in normal operation, as they cause the signals of a number of neighboring masses to be pushed together into a single signal of apparently high resolution. Although the objectives for optimization can be found from this work, the absence of detail it provides about the measuring parameters unfortunately means that it cannot be used for comparison of the success in terms of mass resolution and precision.
The works mentioned above both aim at creating an ideal quadrupolar field distribution for the trapping potential. A field distribution of this type is undoubtedly ideal for small numbers of ions in the measuring cell. It is, however, questionable whether this field distribution is also ideal when a large number of ions, of the order of some tens of thousands up to a hundred thousand ions, are injected into the measuring cell, as is necessary for quantitative analyses.
Additional effects occur if large numbers of ions are injected into the ICR measuring cell. The ions, due to the many elastic impacts with other ions, are again and again pushed to the side by their trapping oscillations, whereby a component of the velocities that were originally aligned with the axis are always converted into cyclotron motions with tiny radii of much less than a millimeter. The impacts between the ions therefore lead, over periods in the order of a second, to a redistribution of the kinetic energy of the originally wide trapping oscillations over the degrees of spatial freedom, similar to thermalization in a collision gas. As a result, the thin, long, cigar-shaped ion cloud is shortened, and the ions do no longer widely oscillate between the trapping electrodes.
If the ions are very heavy, that is if they consist of hundreds of atoms, then semi-elastic impacts may even increase the internal energy, bringing a loss of kinetic energy and thus resulting in a further shortening of the ion cloud. This effect has not, however, yet been investigated; it probably has a very long time constant. An effect of this sort could lead to a kind of “crystallization” of the ions in the ion cloud, as regularly occurs in quadrupole high-frequency ion traps after thermalization of the ion movements with a damping gas. By this crystallization the ions in the cloud are practically confined to a fixed position, and only few exchanges of positions take place.
A further effect that occurs when very high numbers of ions are present in the ICR measuring cell is that ion clouds of very similar masses coalesce in their cyclotron track, resulting in peak coalescence. Following excitation, the clouds of ions of different masses with different cyclotron frequencies orbit around the same cycling track. Ion clouds with almost the same cyclotron frequencies (almost identical masses) thus remain together on this track for relatively long periods. They only separate very slowly and the repelling electrostatic forces between the two clouds act on each other for a very long time. Under the influence of the repelling electrical field, the two clouds begin to rotate (gyrate) around the centroid of their common charge. The cyclotron circulation and this rotation together create cycloidal paths; due to their slightly different cyclotron motion speed, the two clouds are repeatedly brought together again. They lock to one another in this way. The effect depends on the strength of the repulsion between the ion clouds, that is on the number of ions in the two (or more) ion clouds. In this way, the two ion clouds behave as one unit on the cyclotron track, causing a single image signal instead of two separate signals. Thus two (or even more) ICR signals coalesce to a single, often very sharply defined, signal.
Sometimes this peak coalescence involves the different signals from one ion species formed by the different 13C-satellites and which therefore differ by one mass unit. Particularly often it involves the fine structure of these 13C-satellites with one and the same nominal mass unit, but which also contains some of the isotopes 2D, 15N, 18O or 34S, and whose signals can only be separated with a particularly high mass resolution. The ion signals from two different substances having the same nominal mass number can also be affected by this. Particularly sharply defined signals produced by peak coalescence can easily be looked upon as high-resolution ICR signals, but they do not contain correct analytical information, and they falsify the determination of mass.
This peak coalescence usually only occurs when the density of ions is high. Since the clouds of excited ions in the ICR cell have the shape of a thin cigar whose length depends on the trapping potential, the ion density rises if the trapping potential is increased, and coalescence can then occur with a smaller number of ions. It is not known whether peak coalescence also depends on the shape of the ion clouds, the width of the cyclotron tracks or on other parameters.
The cycling frequency of the clouds for each species of ion can be determined from a Fourier transform of the image current transients. The accuracy with which the frequency can be determined always rises with the duration for which the image currents are measured. The times over which cyclotron motion of the ions can be measured are, however, limited; in commercial ICR mass spectrometers they frequently have a maximum of four seconds. Over this period, the amplitude of the image currents (the transient) has usually dropped to such a level that noise predominates, and extending the measuring time no longer brings any improvement to the frequency determination. The mass resolution is therefore also no longer improved.
The vacuum inside the measuring cell must be as good as possible, as the ions must not undergo impacts with residual gas molecules during the image current measurement period. Every impact between an ion and a residual gas molecule puts the ion more or less out of the phase of the other ions with the same charge-related mass. Due to loss of phase homogeneity (coherence) the image current amplitudes decrease and the signal-to-noise ratio continuously deteriorates, so shortening the usable transient duration. The measurement should be taken over at least a few hundred milliseconds, ideally over many seconds. This requires vacua in the range of between 10−7 and 10−9 pascal.
The work of E. N. Nikolaev et al., “Realistic modeling of ion cloud motion in a Fourier transform ion cyclotron resonance cell by use of a particle-in-cell approach” (Rapid Comm. Mass Spectrom. 2007, 21, 1-20) has shown by extensive computer simulations that even in an ideal vacuum, the initially cigar-shaped clouds of ions of the same mass per unit charge change their shape continuously as they circulate. In ICR measuring cells with apertured trapping diaphragms at the ends, the cigar-shaped clouds develop tails from their ends or from the centre, depending on the conditions, and these are dragged along the cycling path behind the clouds. Tails developing from the centre initially create a form reminiscent of a broad tadpole. The tails continue to lengthen until they become entire rings that no longer contribute to the detection of the image currents. The heads of the tadpoles simply become thickenings in the ring-shaped cloud of cycling ions, and gradually disappear entirely. At this point the usable measuring time has come to an end, as the image currents no longer contain any alternating components for this species of ions; it is only from these that the frequencies of the cyclotron rotations can be determined.
The reason why these tails develop has not yet been explained, but probably depends on the space charge of the individual ion clouds in association with the shape of the trapping potentials. Strongly repelling forces are present within the ion clouds and attempt to push the clouds apart. In a strong magnetic field, these forces cause the cloud to gyrate about its own axis; the gyration develops in such a way that the repulsive space charge, the additional centrifugal force, and the Lorenz force are in balance with one another. As a result, variations in density or other effects can lead to imbalances with protuberances. Interestingly, the fact that the various clouds of ions of different masses continuously overtake one another as they cycle, and must therefore repeatedly pass through each other, plays hardly any part.